Tony,
We have been through the exact scenario you described. The insurance company does not cut and run. Especially if you are insured properly. And we came through it (financially, not emotionally) just fine. Still with the same insurance company, still in business 11 years later.

We elected to leave that insurance carrier 4 years after the incident (someone else quoted us substantially lower premiums) and then went back to the same insurance company who covered us through the incident and the aftermath, 3 years after that.